A novel holistic approach for solving the multi-criteria transshipment problem for infectious waste management

* Corresponding author. E-mail address: narong.wi@ksu.ac.th (N. Wichapa) © 2019 by the authors; licensee Growing Science, Canada. doi: 10.5267/j.dsl.2019.5.002 Decision Science Letters 8 (2019) 441–454 Contents lists available at GrowingScience Decision Science Letters homepage: www.GrowingScience.com/dsl A novel holistic approach for solving the multi-criteria transshipment problem for infectious waste management Narong Wichapaa* and Porntep Khokhajaikiatb aDepartment of Industrial Engineering, Faculty of Engineering and Industrial Technology, Kalasin University, Kalasin, 46000, Thailand bDepartment of Industrial Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, 40002,Thailand C H R O N I C L E A B S T R A C T Article history: Received February 2, 2019 Received in revised format: May 2, 2019 Accepted May 14, 2019 Available online May 14, 2019 Effective transshipment network is currently recognized as an important success determinant for most manufacturing organizations, because the transshipment management has significant impact on cost and environmental impact. Due to the complexity of the multi-criteria transshipment problem for infectious waste management (IWM) for this case, forty hospitals and three candidate disposal municipalities in Northeastern Thailand, a novel holistic approach (combination of fuzzy AHP, transshipment model and DEA) was developed for solving this problem. We first utilized the fuzzy AHP technique to calculate the location weights of each candidate disposal municipalities. Secondly, a new cost-based transshipment model was formulated and solved in order to provide the set of feasible solutions. These solutions can be viewed as decision making units (DMUs), inputs and outputs. Finally, DEA-CCR model was applied to calculate the efficiency scores of candidate DMUs. The study results demonstrated that the proposed holistic approach can help decision makers (DMs) to choose a suitable transshipment network for IWM. The major advantage of the proposed holistic approach is that both costs and environmental impacts under constraints are focused on simultaneously. Future work will apply the developed approach with other real-world complex problems to enhance the validity of the research output further. For large-size transshipment problems in which an exact solution cannot be found, meta-heuristics must be applied. .2018 by the authors; licensee Growing Science, Canada© Keywords: Multi-criteria decision making Transshipment problem Fuzzy AHP Data envelopment analysis 1. Introduction Transshipment problem, which form a subgroup of the transportation problem, has become a critical issue in the current logistics and supply chain management. Effective transshipment network management is currently recognized as a key success factor for the competitiveness and success by most sectors. The transshipment problem is similar to the transportation problem which deals with shipping a commodity from an origin to a final destination. In a transshipment problem, the commodities are not sent directly from sources to final destinations, i.e. they pass through at least one intermediate point before reaching the final destination (Gass, 1984). The transshipment problem is a critical area of transportation network management that can enable a transportation network to achieve cost savings by consolidating shipments from several supply points at intermediate points, and then sending them together to demand points. Traditionally, the transshipment problem is one of the single- objective optimization problems. A transshipment network that incurs the lowest total cost is 442 considered as the best transshipment network. Although cost-based transshipment theory has a long history, it seems that the viewpoint of cost alone cannot deal with real-world problems such as networks for waste disposal, networks for nuclear power plants and networks for IWM. One of the most essential difficulties in solving the multi-criteria transshipment problem for IWM is to choose suitable methods for evaluating these complicated decision criteria, such as economic impact, ecological impact, governmental, municipal and environmental regulations (Önüt & Soner, 2008). Undoubtedly, in practice, the viewpoints of costs and other relevant decision criteria need to be considered together in designing a suitable transshipment network for IWM. This is very complex and it is very difficult to choose the best transshipment network because there are several criteria and various regulations that must be considered together. From the literature review, the transshipment model is one of the mathematical models often used for solving optimization problems in various application areas. Certainly, in the transshipment problem for IWM, the viewpoint of cost alone cannot deal with this complex problem. Hence, a traditional transshipment model needs to be adapted for solving this problem. In this research, a novel holistic approach is proposed for handling the multi-criteria transshipment model for IWM. Firstly, the fuzzy Analytical hierarchy Process (AHP) (Saaty, 1980) technique is used to identify the global priority weights for candidate disposal municipalities, which is potentially capable of solving the multi-attribute decision making (MADM) problem with uncertain data and imprecise knowledge. Secondly, a new cost-based transshipment model is formulated and solved to provide the set of feasible solutions, based on the variation of the predetermined number of opened disposal municipalities. According todata envelopment analysis (DEA) (Charnes et al., 1978), these solutions can be viewed as decision making units (DMUs), inputs and outputs. Finally, DEA-CCR model (Charnes et al., 1978) is proposed for calculating the efficiency scores of each DMU in order to rank the candidate alternatives, based on three relevant factors/variables including total cost, number of disposal municipalities and global priority weight of disposal municipalities. Certainly, selecting the proposed holistic approach for solving the multi-criteria transshipment problem for IWM will enhance the confidence of decision making (DMs) in choosing a new transshipment network for IWM. The goals are to obtain the lowest total cost, to obtain the minimum number of opened disposal municipalities and to obtain the maximum total weight processing of opened disposal municipalities under the existing constraints. The combination of the advantages of each technique and ways to overcome their weaknesses are potentially capable of solving real-world complex problems. Therefore, the proposed holistic approach is believed to be more appropriate and applicable than stand-alone methods for a multi-criteria transshipment network design. 2. Literature review Transshipment theory, first introduced by Orden (Orden, 1956), has been extensively applied to solve various optimization problems for over a hundred years. The transshipment problem is an extension of the original transportation problem, in which the shipment of products/goods between the source and the destination is interrupted at one or more intermediate points. The product (such as raw material) is not sent directly from the supplier point to the demand point; rather, it is first transported to a transshipment point, and from there to the demand point (destination). The purpose of the traditional transshipment model is to find the shortest transport route/transportation cost from supplier point in a network to an intermediate point, and then from the intermediate point to a destination point. Later, the transshipment problem has received much attention from many researchers and it has been proposed in a number of various ways in the literature (Alpan et al., 2011; Javaid & Gupta, 2011; Khurana, 2015). Although numerous transshipment models have been studied for a long history, it seems that since the origin of MCDM theory in management sciences, the MCDM theory has been widely used for solving complex real-world problems instead of the stand-alone optimization models in the literature (He et al., 2012; Rezaei et al., 2017). The complex real-world problems cannot be addressed using a cost- based mathematical model alone because there are several criteria and various regulations that must be considered together. Therefore, selecting transshipment network for IWM is one of complex real-world N. Wichapa and P. Khokhajaikiat / Decision Science Letters 8 (2019) 443 problems/ MCDM problems, because it requires integrating relevant criteria, and various regulations must be taken into account. Existing techniques for solving complex real-world problems/MCDM problems can be divided into two categories (Mendoza & Martins, 2006; Wallenius et al., 2008): (1) including Multi-Attribute Decision Making (MADM) and (2) Multi-Objective Decision Making (MODM)/Multi-Objective Programming (MOP). MADM implicate the selection of the best alternative based on the known attributes of a limited number of pre-specified alternatives, whereas MODM implicate the selection of the suitable alternative that meets the DM’s desires (Scott et al., 2012). In MODM, the feasible solutions are usually very large and the suitable alternative will be the one which meets DM’s constraints and priorities. There are various MCDM techniques for solving the real-world complex problems in the different fields. Some of the MADM techniques which are widely applied to solve MADM problems are, AHP, DEMATEL, TOPSIS, ELECTRE, SAW, PROMETHEE, ANP and UTA method (Saaty, 2008). Some of the basic MODM techniques are goal programming (GP), weighting method and e-constraint (Banasik et al., 2018). Both MODM and MADM techniques have been widely used to support decision making in MCDM problems in many fields, depending on the case under study and the scope of the analysis. Additionally, each existing MCDM technique differs in complexity and model characteristics. Although there are many traditional techniques used to tackle MADM problems, AHP is often used to deal with real-world complex problems in the literature (Abdollahzadeh et al., 2016; Al-Harbi, 2001). AHP is one of most powerful and flexible techniques for handling MADM problems with crisp numbers (Karasakal & Aker, 2017; Mobaraki et al., 2014; Unutmaz Durmuşoğlu, 2018). For this reason, AHP techniques have been applied in a wide variety of application areas in the literature. However, due to insufficiency of information, especially for values of qualitative attribute, generally it cannot be expressed by crisp numbers, and some of them are easier to be manifested by fuzzy numbers (Liu et al., 2017). The fuzzy set theory of Zadeh (1965) has been widely applied to deal with uncertainty and fuzziness in the MADM process, and nowadays the fuzzy MADM techniques, such as fuzzy ANP and fuzzy AHP, have often been used to replace traditional MADM techniques in dealing with uncertain data and imprecise knowledge. The main advantages of fuzzy AHP are that the consistency ratio can be measured, and, it can apply to both tangible and intangible criteria (Durán & Aguilo, 2008). However, the disadvantages of fuzzy AHP are that consistency is difficult to achieve when there are too many criteria and alternatives. Thus the fuzzy AHP is potentially capable of solving complex real- world problems with uncertain data and imprecise knowledge. These are the major reasons why the fuzzy AHP technique is chosen as a suitable technique for predetermining the location weights of candidate disposal municipalities in this research. The frontier approach was described by Farrel in 1957 (Farrell, 1957), but a mathematical model for measuring relative efficiency was first introduced as the DEA-CCR model by Charnes et al. (1978). The DEA technique defines the relative efficiency of a group of homogeneous DMUs on the basis of various input- output variables, using mathematical model (Hosseinzadeh Lotfi et al., 2013). Generally, a DMU will be efficient if it obtains the maximum score of 1; otherwise DMUs are inefficient. In recent years a variety of application areas of DEAs have been applied widely in various forms to evaluate the performance of such entities as hospitals, business firms, universities, regions, etc. (Asandului et al., 2014; Ennen & Batool, 2018; Fazlollahi & Franke, 2018; Hosseinzadeh-Bandbafha et al., 2018; Khushalani & Ozcan, 2017; Leleu et al., 2014). DEA is one of the MADM techniques and the relationship between DEA and MADM has been highlighted by a group of researchers (Doyle & Green, 1993; Hu et al., 2017; Lin et al., 2011, 2017; Sinuany-Stern et al., 2000; Stewart, 1996). It has been recognized that the MADM and DEA techniques coincide if input and output variables can be viewed as decision criteria, and DMUs can be viewed as alternatives (Hu et al., 2017; Stewart, 1996). DEA technique is becoming a popular technique since it has the following practical advantages (Fan et al., 2017; Hosseinzadeh Lotfi et al., 2010; Wang et al., 2016): (1) DEA technique is appropriate for evaluating the effectiveness of multiple criteria (multiple inputs and multiple outputs); (2) DEA technique does not require to carry out non-dimensional treatment on the parameters; (3) DEA technique does not need experts to provide weight-related information, because the weights for each variable (Both inputs and outputs) can be gained through mathematical mode; (4) 444 The relationship between input variables and output variables does not need to be considered in the DEA technique and (5) DMUs can be production units, universities, schools, bank branches, hospitals, power plants, etc. However, some of the disadvantages of DEAs are as follows (Berg, 2010): (1) Results of DEA technique are sensitive to the selection of both inputs and outputs; (2) The best specification cannot be tested and (3) If the number of variables are increased, the number of efficient DMUs tends to increase. The various DEAs have been applied continuously in many application areas because of the advantages of this method. However, one of the disadvantages of DEA is that it cannot rank efficient DMUs, because the efficiency scores of all efficient DMUs are the same value (efficiency score =1), so other methods (Falagario et al., 2012; Hou et al., 2018) should be used to solve such problems. For this reason, we are motivated to apply DEA to calculate the efficiency scores for ranking all DMUs. These are the major reasons why DEA is chosen as a technique for calculating the efficiency scores of each DMU, in order to rank all DMUs in this paper. The rest of this research is organized as follows. Literature review, Methodology and Application example are presented in Sections 2, 3 and 4 respectively. Finally, Section 5 is the Conclusion. 3. Methodology When selecting a suitable new transshipment network for IWM, the selection process should have an approach that is appropriate and flexible, and the approach must be able to solve the problem effectively. Therefore, this section presents a holistic approach for solving a multi-criteria transshipment network for IWM. Details of the study framework are demonstrated in Fig. 1. Fig.1. The study framework M ak in g of F uz zy A H P- ba se d ca lc ul at io ns So lv in g th e co st -b as ed tra ns sh ip m en t m od el Study relevant information to define main criteria, sub-criteria and alternatives Literature review Construct fuzzy relative importance using TFNs between criteria of each level using fuzzy AHP Estimate fuzzy priority weights of matrices Expert opinions Check the consistency No CR≤0.10  Yes  Calculate the global priority weights of each candidate disposal municipality. Formulate and solve the cost-based transshipment model for IWM to provide candidate alternatives Take the candidate alternatives as DMUs and input-output variables into DEA technique Select a suitable network for IWM, based on DEA technique N et w or k se le ct io n N. Wichapa and P. Khokhajaikiat / Decision Science Letters 8 (2019) 445 3.1 Fuzzy AHP AHP has been proposed by Saaty (Saaty, 1980; Saaty, 1977). It is one of most powerful and flexible techniques for handling MADM problems. However, the use of AHP's discrete scale cannot handle the ambiguity and uncertainty in deciding on different attributes priorities (Choudhary & Shankar, 2012). Hence, the fuzzy AHP technique has been widely employed for addressing MADM problems instead of original AHP in the literature. In this research, the location weights of candidate disposal municipalities will be evaluated using the same method as Wichapa (Wichapa & Khokhajaikiat, 2017b). 3.2 A cost-based transshipment model for IWM The transshipment problem is a multi-phase transportation problem, in which the flow of goods or products between the source and the destination is interrupted at one or more points. The goods do not need to send directly from the origin to the destination; rather, they are first transported to a transshipment point, and from there to the destination. Therefore, a transshipment model for IWM that differs from the traditional transshipment models in the literature is formulated to choose various size incinerators, various size stores, multiple candidate transshipment hospitals and multiple candidate disposal municipalities. Details of cost-based transshipment model for IWM are shown below. Fig.2. A transshipment network for IWM Indices: i is hospitals, i = 1, 2 , ... , I (I=40). j is candidate transshipment hospitals, j = 1, 2 ,..., J (J=40). k is candidate disposal municipalities, k = 1, 2 , ... , K (K=3). Parameters: u is the value of unit transportation cost (baht/km). dt1ij is actual distance between hospital i and candidate transshipment hospital j. dt2ik is actual distance between hospital i and candidate disposal municipality k dt3jk is actual distance between candidate transshipment hospital j and candidate disposal municipality k. fsm is facility and operating costs of storage at stores m, m = 1, 2 , ... , M (M = 2). fdn is facility and operating costs of incinerator n, n = 1, 2 , ... , N (N = 2). di is the demand of the hospital i (kg/day). dsj is the storage requirement of the opened transshipment hospital j (kg/day). csm is the storage capacity m (kg /day). cdn is the incinerator capacity n (kg /day). p is the number of disposal municipalities to be located. H4 H2  H1  H4 H2 H1 D1 D2 D3  446 Decision variables: X1ij is a binary variable; X1ij = 1 if the waste materials are delivered from hospital i to candidate transshipment hospital j; X1ij = 0 otherwise. X2ik is a binary variable; X2ik = 1 if the waste materials are delivered from hospital i to candidate disposal municipality k; X2ik = 0 otherwise. X3jk is a binary variable; X3jk = 1 if the waste materials are delivered from candidate transshipment hospital j to candidate disposal municipality k; X3jk = 0 otherwise. Yjm is a non-negative variable; Yjm = 1 if candidate transshipment hospital j is selected by using the size of storage m, Yjm = 0 otherwise. Zkn is a non-negative variable; Zkn = 1 if candidate disposal municipality k is selected by using the size of incinerator n, Zkn = 0 otherwise. Objective function:               J j K k jkjk I i K k ikik I i J j ijijkn K k N n njm J j M m m XdtuXdtu XdtuZfdYfsGMin 1 11 1 1 11 11 1 3322 11∑∑∑∑ (